Abstract
Let T be a weak torsion class of left R-modules and n a positive integer. A left R-module M is called (T, n)-injective if Ext (C, M) = 0 for each (T, n + 1)-presented left R-module C; a right R-module M is called (T, n)-flat if Tor (M, C) = 0 for each (T, n +1)-presented left R-module C; a left R-module M is called (T, n)-projective if Ext (M, N) = 0 for each (T, n)-injective left R-module N; the ring R is called strongly (T, n)-coherent if whenever 0 → K → P → C → 0 is exact, where C is (T, n + 1)-presented and P is finitely generated projective, then K is (T, n)-projective; the ring R is called (T, n)-semihereditary if whenever 0 → K → P → C → 0 is exact, where C is (T, n + 1)-presented and P is finitely generated projective, then pd(K) ⩽ n → 1. Using the concepts of (T, n)-injectivity and (T, n)-flatness of modules, we present some characterizations of strongly (T, n)-coherent rings, (T, n)-semihereditary rings and (T, n)-regular rings.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
